Problem: What do the following two equations represent? $2x-3y = -3$ $-6x+9y = 4$
Explanation: Putting the first equation in $y = mx + b$ form gives: $2x-3y = -3$ $-3y = -2x-3$ $y = \dfrac{2}{3}x + 1$ Putting the second equation in $y = mx + b$ form gives: $-6x+9y = 4$ $9y = 6x+4$ $y = \dfrac{2}{3}x + \dfrac{4}{9}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.